Mathematical models have been developed to describe hormone-receptor interactions in complex cases involving heterogeneity of hormone and receptor, positive and/or negative cooperativity, and failure to achieve equilibrium or steady-state conditions. By use of computer simulations and curve-fitting techniques, we have studied the role of cooperativity in binding of insulin to its receptors on lymphocytes; binding of catecholamines and their synthetic analogs to erythrocytes and erythrocyte membranes; and binding of hCG to rat Leydig cells. A new method has been developed which can, at least in principle, permit calculation of affinity constants, binding capacities, and allow construction of Scatchard plots, without the use of radioisotopes. The effect of factors such as thresholds, spare receptors, and cooperativity on the shape of dose response curves has been analyzed by simulation techniques. We have employed the Monod-Wyman-Changeux model as a basis for describing the complex interactions in hormone-sensitive adenylate cyclase systems. BIBLIOGRAPHIC REFERENCES: Brown, E.M., Fadak, S.A., Woodard, C.J. Aurbach, G.C. and Rodbard, D., Beta Receptor Interactions: Direct Comparison of Receptor Interactions and Biological Activity, J. Biol. Chem., 251, 1239-1245, 1976. Ranke, M.B., Stanley, C.A., Rodbard, D., Baker, L., Bongiovanni, A.M., and Parks, J.S., Sex Differences in the Binding of Human Growth Hormone to Isolated Rat Hepatocytes, Proceedings of the National Academy of Sciences, U.S., 73, 847-851, 1976.